A327596 Number of colored compositions of 2n using all colors of an n-set such that all parts have different color patterns and the patterns for parts i are sorted and have i colors in (weakly) increasing order.

1, 1, 27, 1222, 78819, 7990555, 1075539168, 185948116920, 39826324710186, 10231314625984628, 3097070454570888110, 1088018981038197792790, 436918864329884469153204, 198400793333371519398942287, 100941775818744369615731919906, 57064609834208008799145534143376

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Formula

a(n) = A327244(2n,n).

Maple

C:= binomial:
b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
      b(n-i*j, min(n-i*j, i-1), k, p+j)/j!*C(C(k+i-1, i), j), j=0..n/i)))
    end:
a:= n-> add(b(2*n$2, i, 0)*(-1)^(n-i)*C(n, i), i=0..n):
seq(a(n), n=0..17);

Mathematica

c = Binomial;
b[n_, i_, k_, p_] := b[n, i, k, p] = If[n == 0, p!, If[i < 1, 0, Sum[
    b[n-i*j, Min[n-i*j, i-1], k, p+j]/j!*c[c[k+i-1, i], j], {j, 0, n/i}]]];
a[n_] := Sum[b[2n, 2n, i, 0]*(-1)^(n-i)*c[n, i], {i, 0, n}];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Apr 11 2022, after Alois P. Heinz *)

Crossrefs

Cf. A327244.

Sequence in context: A223552 A357228 A104206 * A163568 A066300 A273518

Adjacent sequences: A327593 A327594 A327595 * A327597 A327598 A327599

Keyword

nonn

Author

Alois P. Heinz, Sep 18 2019

Status

approved